Ionization Energy Loss

For a heavy (M>m_e), fast (b> a) charged (Q=ze) particle, the ionization energy loss per unit distance travelled in a medium is given by:

Where:

n	density of electrons in medium
I	effective ionization potential of atoms in medium
d	"density effect" due to screening of charged particle's electromagnetic field by polarization of atoms in medium d Æ 2 ln(g) + constant for g>>1
C/Z	"shell corrections" important when b ª batomic electronsªa
n	higher order QED corrections important when b ª a

Measured ionization energy loss measured in ARGUS experiment
atmospheric pressure propane drift chamber.

Bremsstrahlung

All charged particles scatter from the atomic nuclei and electrons when passing through a medium. When a charged particle is accelerated it radiates, so scattering of charged particles produces radiation. The radiation produced by charge particles passing through a medium is know as "bremsstrahlung".

The mean bremstrahlung energy loss of a charged particle (mass M, charge ze) is

where the radiation length, X₀, for the medium (atom density n_a and atomic number Z) is approximately given by

Pair production

Real photons spend part of their time (about 1/a) as a virtual electron-positron pair. These virtual e+e- pairs can scatter from the virtual photons in the electromagnetic field of a charged particle, e.g. an atomic nucleus or electron, and become a real e+e- pair.

In the high energy limit (Eg>>2me), the mean distance a photon will travel before pair producing is

Xp 9/7 X₀

(Note: The reason the radiation length and the pair production length are almost the same is because bremsstrahlung and pair production are simply time and space rearrangements of the same process: a real photon coupling to an electron which is coupled via a virtual photon to a nucleus.)